```On Jan 6, 2:54=A0pm, Jerry Avins <j...@ieee.org> wrote:
> Clay wrote:
> > On Jan 5, 5:26 pm, "carlierm" <carliermon...@gmail.com> wrote:
> >> Hi,
>
> >> I need to extract the envelope of an audio signal and do some changes =
in
> >> its spectum of magnitude, and then I need to reconstruct the signal an=
d
> >> take it to the time domain. =A0I thing thatt I can do that taking the =
hilbert
> >> transform of the original signal, =A0find the magnitu and perform the
> >> changes; but what i do not know is how to go back to the time domain. =
=A0How
> >> to take the inverse of the hilbert transform? Any sugestions?
>
> >> I will appreciate very much any help.
>
> >> Monica
>
> > H^-1(f(t)) =3D -H(f(t))
>
> Clay, maybe you can tell me what the envelope of an audio signal -- say,
> the output of a microphone -- is. I imagine it as the output as a VU
> meter, but that doesn't fit the question.
>
> Jerry
> --
> Engineering is the art of making what you want from things you can get.- =
Hide quoted text -
>
> - Show quoted text -

Yes it is like a VU meter. Of course for standard AM, the envelope
minus the DC offset is the data of interest. I don't know all of what
the OP desires, so we'll have to wait on more clarification.

With Hilbert transforms being mentioned, one assumes analytic signals
are involved and then the magnitude of the analytic signal is the
instantaneous amplitude. The OP mentions some intermediate operations
before the inverse Hilbert is applied, so who knows?

Clay

```
```Clay wrote:
> On Jan 5, 5:26 pm, "carlierm" <carliermon...@gmail.com> wrote:
>> Hi,
>>
>> I need to extract the envelope of an audio signal and do some changes in
>> its spectum of magnitude, and then I need to reconstruct the signal and
>> take it to the time domain.  I thing thatt I can do that taking the hilbert
>> transform of the original signal,  find the magnitu and perform the
>> changes; but what i do not know is how to go back to the time domain.  How
>> to take the inverse of the hilbert transform? Any sugestions?
>>
>> I will appreciate very much any help.
>>
>> Monica
>
> H^-1(f(t)) = -H(f(t))

Clay, maybe you can tell me what the envelope of an audio signal -- say,
the output of a microphone -- is. I imagine it as the output as a VU
meter, but that doesn't fit the question.

Jerry
--
Engineering is the art of making what you want from things you can get.
&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
```
```On Tue, 05 Jan 2010 18:58:56 -0600, "steveu" <steveu@coppice.org>
wrote:

[Snipped by Lyons]
>
>I've used a check that 4 Hilberts in a row gets you roughly where you
>started as a sanity test for a Hilbert implementation.
>
>Steve

Hi,
right you are!  And three Hilbert transforms
in a row yields the inverse Hilbert transform.

[-Rick-]
```
```On Jan 5, 5:26=A0pm, "carlierm" <carliermon...@gmail.com> wrote:
> Hi,
>
> I need to extract the envelope of an audio signal and do some changes in
> its spectum of magnitude, and then I need to reconstruct the signal and
> take it to the time domain. =A0I thing thatt I can do that taking the hil=
bert
> transform of the original signal, =A0find the magnitu and perform the
> changes; but what i do not know is how to go back to the time domain. =A0=
How
> to take the inverse of the hilbert transform? Any sugestions?
>
> I will appreciate very much any help.
>
> Monica

H^-1(f(t)) =3D -H(f(t))

```
```>On Tue, 05 Jan 2010 16:26:06 -0600, carlierm wrote:
>
>> Hi,
>>
>> I need to extract the envelope of an audio signal and do some changes
in
>> its spectum of magnitude, and then I need to reconstruct the signal
and
>> take it to the time domain.  I thing thatt I can do that taking the
>> hilbert transform of the original signal,  find the magnitu and
perform
>> the changes; but what i do not know is how to go back to the time
>> domain.  How to take the inverse of the hilbert transform? Any
>> sugestions?
>>
>> I will appreciate very much any help.
>>
>> Monica
>
>(A)  Unless I'm quite mistaken, the Hilbert transform is it's own
>inverse, give or take a sign change -- since it is defined as that which

>shifts the phase of all components with positive frequencies by +90
>degrees, and the phase of all components with negative frequencies by -90

>degrees, doing it again will get you the negative of what you started out

>with.
>
>(B)  A Hilbert-transformed signal already is in the time domain.
>
>(C)  What is your end goal?  You obviously are confused about the bark on

>the tree you're inspecting -- do you know the shape of your forest?
>
>--
>www.wescottdesign.com

I've used a check that 4 Hilberts in a row gets you roughly where you
started as a sanity test for a Hilbert implementation.

Steve
```
```carlierm wrote:
> Hi,
>
> I need to extract the envelope of an audio signal and do some changes in
> its spectum of magnitude, and then I need to reconstruct the signal and
> take it to the time domain.  I thing thatt I can do that taking the hilbert
> transform of the original signal,  find the magnitu and perform the
> changes; but what i do not know is how to go back to the time domain.  How
> to take the inverse of the hilbert transform? Any sugestions?
>
> I will appreciate very much any help.

The "envelope" of an audio signal is not (as far as I know) a well
defined term. If you could explain what you mean by it, I'll try to

Jerry
--
Engineering is the art of making what you want from things you can get.
&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
```
```On Tue, 05 Jan 2010 16:26:06 -0600, carlierm wrote:

> Hi,
>
> I need to extract the envelope of an audio signal and do some changes in
> its spectum of magnitude, and then I need to reconstruct the signal and
> take it to the time domain.  I thing thatt I can do that taking the
> hilbert transform of the original signal,  find the magnitu and perform
> the changes; but what i do not know is how to go back to the time
> domain.  How to take the inverse of the hilbert transform? Any
> sugestions?
>
> I will appreciate very much any help.
>
> Monica

(A)  Unless I'm quite mistaken, the Hilbert transform is it's own
inverse, give or take a sign change -- since it is defined as that which
shifts the phase of all components with positive frequencies by +90
degrees, and the phase of all components with negative frequencies by -90
degrees, doing it again will get you the negative of what you started out
with.

(B)  A Hilbert-transformed signal already is in the time domain.

(C)  What is your end goal?  You obviously are confused about the bark on
the tree you're inspecting -- do you know the shape of your forest?

--
www.wescottdesign.com
```
```Hi,

I need to extract the envelope of an audio signal and do some changes in
its spectum of magnitude, and then I need to reconstruct the signal and
take it to the time domain.  I thing thatt I can do that taking the hilbert
transform of the original signal,  find the magnitu and perform the
changes; but what i do not know is how to go back to the time domain.  How
to take the inverse of the hilbert transform? Any sugestions?

I will appreciate very much any help.

Monica

```